Adaptive measurement strategy for quantum subspace methods

Estimation of physical observables for unknown quantum states is an important problem that underlies a wide range of fields, including quantum information processing, quantum physics, and quantum chemistry. In the context of quantum computation, in particular, existing studies have mainly focused on holistic state tomography or estimation on specific observables with known classical descriptions, while this lacks the important class of problems where the estimation target itself relies on the measurement outcome. In this work, we propose an adaptive measurement optimization method that is useful for the quantum subspace methods, namely the variational simulation methods that utilize classical postprocessing on measurement outcomes. The proposed method first determines the measurement protocol based on QSE calculation for classically simulatable states, and then adaptively updates the protocol according to the quantum measurement result. As a numerical demonstration, we have shown for excited-state simulation of molecules that (i) we are able to reduce the number of measurements by an order of magnitude by constructing an appropriate measurement strategy (ii) the adaptive iteration converges successfully even for strongly correlated molecule of H$_4$. Our work reveals that the potential of the QSE method can be empowered by elaborated measurement protocols, and opens a path to further pursue efficient quantum measurement techniques in practical computations.Comment: 9 pages, 4 figure

神経誘導因子Netrin-1は軟骨形成や骨形成においてBMPまたはNogginにより調節される

This is the first report describing neurogenic factor of Netrin-1 related to chondrogenesis or osteogenesis in a human cells. Netrin is a morphogenetic factor that induces a growth cone of an axial filament of the nervous system. However, the roles of Netrin in chondrogenesis or osteogenesis are not yet understood. We analyzed the relationship between Netrin and bone morphogenetic protein-2 (BMP-2) in chondrogenesis or osteogenesis, using a human chondrocyte-like cell line (USAC), which also retains multi-potency to differentiate into osteoblasts and adipocytes. Netrin-1 mRNA was decreased in USAC cells, though the expression was increased during osteogenic differentiation at the stage when osteocalcin mRNA were increased by BMP-2. Furthermore, inhibition of Netrin-1 gene increased Cbfa1 mRNA expression, and decreased Sox9 mRNA expression. We also found that Netrin-1was strongly expressed in immature chondrocytes of cartilage-like tissues that were formed in an exo vivo experiment with diffusion chambers. The se findings indicate that Netrin-1 and BMP-2 regulates in the stage dependent process of mesenchymal cell differentiation to chondrocytes or osteoblasts.骨芽細胞または脂肪細胞への分化多能を保持するヒト軟骨細胞様細胞系(USAC)を用い、軟骨形成または骨形成におけるNetrinと骨形成蛋白質-2(BMP-2)との関係を調べた。Netrin-1 mRNAはUSAC細胞中では減少するが、オステオカルシンmRNA濃度がBMPによって上昇する際の骨芽細胞分化時にNetrin-1 mRNAの発現が増加した。Netrin-1遺伝子を阻害すると、Cbfal mRNA発現は増加しSox9 mRNA発現は減少した。またNetrin-1は軟骨様組織の未成熟軟骨細胞において強く発現した。Netrin-1とBMP-2が、間葉細胞の軟骨細胞または骨芽細胞へ分化プロセスを制御すると考えた